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Re: Plot function at specific points

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114114] Re: Plot function at specific points
  • From: "István Zachar" <replicatorzed at gmail.com>
  • Date: Wed, 24 Nov 2010 06:58:05 -0500 (EST)

This is indeed a cheater solution : )
And a twofolded cheater, though rather clever: first, it is messy in the
sense that the eps threshold is something arbitrary, and second, it
still goes over the 10000 iterations - something that I definitely want
to avoid if I have a set of explicit query-points.
I'm sure that somehow the plotting algorithm can be instructed via the
Method option to sample at specific locations, though I still haven't
found any info about such possibilities. In the meantime I've crafted
the following workaround, following the v6 extension of Table to list
iterators:

f == Interpolation[{{0, 1}, {1, 2}, {2, 3}, {3, 5}, {4, 8}, {5, 5}, {6,
2}, {7, 1}, {8, 1}, {9, 2}, {10, 4}}];
g == Interpolation[{{0, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}, {5, 4}, {6,
3}, {7, 2}, {8, 1}, {9, 1}, {10, 0}}];
lowRes == Range[0, 10, 2];

Unprotect[Plot];
Plot[func_, {x_, range_}, opts___] /; MatchQ[range, {__?NumericQ}] :==
ListPlot[
         Transpose@Outer[{#1, #2[#1]} &, range, If[ListQ@func, func,
{func}]], opts, Joined -> True];
Protect[Plot];

Plot[{f, g}, {x, lowRes}]
Plot[g, {x, lowRes}]


I see no objection why this extension shouldn't be part of v9 in the
future (or even of v8.0.1) : )
Of course some proper option-handling must be added as well, and it must
be extended to LogPlot and relatives,
but I think I'll use this until someone can reveal the scope of Method
inside Plot.

Thanks again for the suggestions,

Istvan



On 2010.11.23. 14:51, Leonid Shifrin wrote:
> Hi Istvan,
>
> You are likely to get much better solutions, but here is one way
> (cheating somewhat):
>
> f == Interpolation[{{0, 1}, {1, 2}, {2, 3}, {3, 5}, {4, 8}, {5, 5}, {6,
>       2}, {7, 1}, {8, 1}, {9, 2}, {10, 4}}];
> lowRes == Range[0, 10, 2];
> eps == 0.001;
> cutF == Function[
>    Evaluate[
>     Module[{x},
>      Total[UnitStep[x - # + eps]*UnitStep[# + eps - x] & /@
>         lowRes] /. x -> #]]];
> Plot[f[x]*cutF[x], {x, 0, 10}, PlotRange -> {{0, 10}, {0, 9}},
>  PlotPoints -> 10000, PlotStyle -> {Thickness[0.005]}]
>
> If your f[x] is expensive to compute, you can define f[x]cutF[x] as a
> single function and
> compute f[x] lazily only when cutF[x] is non-zero.
>
> Regards,
> Leonid
>
>
> 2010/11/23 Istv=E1n Zachar <zac at freemail.hu <mailto:zac at freemail.hu>>
>
>     Dear Group,
>
>     is there a method to plot an InterpolatingFunction at specific pointr
>     WITHIN Plot? I am of course aware that I can use ListPlot at any time=
,
>     though for certain reasons I have to stick with Plot. The main reason
>     is that I have a large amount of InterpolatingFunctions which I plot
>     with Plot as default, though at request I have to plot the same
>     InterpolatingFunctions at different resolutions. PlotPoints and
>     MaxRecursion is no good here, since lower resolution has to use a
>     certain set of x-values, defined prior to plotting. Obviously I want
>     to use the same Plot setup for both high and low-resolution cases.
>     Below is a toy modell of the problem:
>
>     f == Interpolation[{{0, 1}, {1, 2}, {2, 3}, {3, 5}, {4, 8}, {5, 5}, {=
6,
>     2}, {7, 1}, {8, 1}, {9, 2}, {10, 4}}];
>     lowRes == Range[0, 10, 2];
>     Plot[f[x], {x, 0, 10}, PlotRange -> {{0, 10}, {0, 9}}]
>     ListLinePlot[{#, f@#} & /@ lowRes, PlotRange -> {{0, 10}, {0, 9}}]
>
>     Again, what I want is to have a specific Plot call instead of the
>     ListLinePlot, but with same result as ListLinePlot.
>     Note that values of 'lowRes' may not correspond the exact x-
>     coordinates supplied to f.
>
>     Is there a way to tell Plot explicitly the steps to use? Any idea?
>
>     Istvan
>
>


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